A number is doubled and 9 is added. The result is then tripled to obtain 75. What is the original number?

Introduction: This is a straightforward linear transformation problem. Translate the operations into an algebraic equation in the original number and solve.

Given Data / Assumptions:

• Let the original number be n.
• Compute: result = 3*(2n + 9) = 75.

Concept / Approach: Expand and solve for n. All steps involve basic algebra without pitfalls if order of operations is followed carefully.

Step-by-Step Solution:

Verification / Alternative check: Double 8 → 16; add 9 → 25; triple → 75, matches exactly.

Why Other Options Are Wrong: 3.5, 6, 7 do not satisfy the equation; “None of these” is incorrect since 8 fits perfectly.

Common Pitfalls: Misapplying tripling before addition or misreading the operation order.

Final Answer: 8